Table classifying subgroups up to automorphisms

TABLE SORTING AND INTERPRETATION: Note that the subgroups in the table below are sorted based on the powers of the prime divisors of the order, first covering the smallest prime in ascending order of powers, then powers of the next prime, then products of powers of the first two primes, then the third prime, then products of powers of the first and third, second and third, and all three primes. The rationale is to cluster together subgroups with similar prime powers in their order. The subgroups are not sorted by the magnitude of the order. To sort that way, click the sorting button for the order column. Similarly you can sort by index or by number of subgroups of the automorphism class.

The quaternion group of the form PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]

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Linear representation theory

GAP implementation

Group ID

This finite group has order 48 and has ID 28 among the groups of order 48 in GAP's SmallGroup library. For context, there are 52 groups of order 48. It can thus be defined using GAP's SmallGroup function as:

SmallGroup(48,28)

For instance, we can use the following assignment in GAP to create the group and name it :

gap> G := SmallGroup(48,28);

Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:

IdGroup(G) = [48,28]

or just do:

IdGroup(G)

to have GAP output the group ID, that we can then compare to what we want.